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Roots of Unity

Roots of Unity
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2020-11-11 14:29
SequenceCoordinate GeometryComplex Number
This example demonstrates the concept of roots of unity, which are complex numbers on the unit circle that satisfy z^n = 1. Using GeoGebra commands Sequence and Element, a set of roots of unity is constructed. This example involves core concepts of complex numbers and coordinate geometry, suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Sequence(cos(((2 * k) * π / n)) + (ί * sin(((2 * k) * π / n))), k, 0, n - 1) → list1
  2. Sequence(Segment[(0, 0), Element[list1, j]], j, 1, n) → list3
  3. Element(list1, A1) → B1
  4. Element(list1, A2) → B2
  5. Element(list1, A3) → B3
  6. Element(list1, A4) → B4
  7. Element(list1, A5) → B5
  8. Element(list1, A6) → B6
  9. Element(list1, A7) → B7
  10. Element(list1, A8) → B8
  11. Element(list1, A9) → B9
  12. Element(list1, A10) → B10
  13. Element(list1, A11) → B11
  14. Element(list1, A12) → B12
  15. Element(list1, A13) → B13
  16. Element(list1, A14) → B14
  17. Element(list1, A15) → B15
  18. Element(list1, A16) → B16
  19. Element(list1, A17) → B17
  20. Element(list1, A18) → B18
  21. Element(list1, A19) → B19
  22. Element(list1, A20) → B20

AI Drawing Prompt Reference

Draw a unit circle with n equally spaced points on its circumference, representing the n-th roots of unity. Connect each point to the center with a straight line segment, creating a radial star-like pattern. All points lie on the circle, with equal angular spacing, resulting in a symmetric and periodic figure.
The prompt above was compiled from the original drawing commands and is for reference only.